Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨? 3 ⋯ (?+3) ⋯ 0 ⋯⟩ (?≠3,0)
⟨ ⁶ᵗʰa ³ʳᵈb ⟩, min⟦a,b⟧ = 0
6th → a, 2nd → b, a+b=6
⟨ ¹ˢᵗa ⁰ᵗʰb ⟩, (ab)₁₀ ≤ 25
#125034_v2.5
Originating from a math proof, 125034 is a game driven by combinatorics, logic, and probability.
2024-05-31 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨? 0 ⋯ (?−1) ⋯ 2 ⋯⟩ (?≠1)
5th → a, 4th → b, a+b=5
⛔Avoid
{p3, p2, p1} = ? + {0,2,3}
{p3, p1, p0} = ? + {0,1,3}
⟨ ³ʳᵈa ²ⁿᵈb ⟩, min⟦a,b⟧ = 2
⟨ ²ⁿᵈa ⁰ᵗʰb ⟩, max⟦a,b⟧ = 4
#125034_v2.5
2024-05-30 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
Sim⟨ ⁶ᵗʰ3 ⁵ᵗʰ6 ⁴ᵗʰ2 ³ʳᵈ4 ²ⁿᵈ1 ¹ˢᵗ0 ⁰ᵗʰ5 ⟩ ≥ 1
⟨ ⁶ᵗʰc ⁵ᵗʰa ⁰ᵗʰb ⟩, a > b > c
2nd → a, 1st → b, |a-b|=3
6th → a, 3rd → b, ab=0
⛔Avoid
⟨⋯ 6 ⋯ 5 ⋯⟩
⟨ ⁶ᵗʰa ⁴ᵗʰb ³ʳᵈc ⟩, (abc)₁₀ ≤ 246
#125034_v2.5
2024-05-30 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
Sim⟨ ⁵ᵗʰ1 ⁴ᵗʰ2 ³ʳᵈ3 ²ⁿᵈ4 ¹ˢᵗ0 ⁰ᵗʰ5 ⟩ = 1
1st → 1
⛔Avoid
⟨⋯ 3 ⋯ a ⋯⟩, a = 1|4
Jump(1,5) = 2
3rd → 5
⟨⋯ a ⋯ 2 ⋯⟩, a = 0|1|3|5
#125034_v2.5
2024-05-28 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 2 ⋯ 4 ⋯ 3 ⋯⟩
Jump(1,4) = 1
5th → a, 3rd → b, |a-b|=4
⛔Avoid
2nd → 2|3|4|5|6
5th|4th|3rd → 2
#125034_v2.5
2024-05-28 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨? 3 ⋯ (?+1) ⋯ 0 ⋯⟩ (?≠3,2)
3rd → 1|3|4
⛔Avoid
⟨⋯ 1 ⋯ 5 ⋯ 2 ⋯⟩
⟨? ⋯ 4 ⋯ (?+1) ⋯⟩ (?≠4,3)
#125034_v2.5
2024-05-26 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨? 6 ⋯ (?−3) ⋯ 2 ⋯⟩ (?≠6)
⟨ ⁶ᵗʰ↓ ⁵ᵗʰ↓ ⁴ᵗʰ↑ ³ʳᵈ↑ ²ⁿᵈ= ¹ˢᵗ↑ ⁰ᵗʰ↓ ⟩ after 6−⟨⋯⟩
⟨ ²ⁿᵈa ⁰ᵗʰb ⟩, max⟦a,b⟧ = 5
⛔Avoid
⟨ ⁴ᵗʰa ⁰ᵗʰb ⟩, (ab)₁₀ ≥ 12
#125034_v2.5
2024-05-26 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
{p5, p2, p1} = ? + {0,1,2}
5th → a, 0th → b, a+b=2
3rd → a, 1st → b, a+b=9
#125034_v2.5
2024-05-24 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
1st → a, 0th → b, a+b=1+6n
6th → 0|1|3
⟨ ⁶ᵗʰ= ⁵ᵗʰ= ⁴ᵗʰ↑ ³ʳᵈ↓ ²ⁿᵈ↑ ¹ˢᵗ= ⁰ᵗʰ= ⟩ after 6−⟨⇌⟩
⛔Avoid
2nd → a, 0th → b, ab=2+5n
5th → a, 1st → b, |a-b|=2
#125034_v2.5
2024-05-24 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁵ᵗʰ↓ ⟩ after 2×⟨→⟩
⛔Avoid
⟨⋯ 3 ⋯ a ⋯⟩, a = 0|5
⟨⋯ a ⋯ 5 ⋯⟩, a = 2|4
⟨ ⁵ᵗʰa ⁰ᵗʰb ⟩, (ab)₁₀ ≥ 42
Jump(2,3) = 1
#125034_v2.5
2024-05-23 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
{p5, p1, p0} = ? + {0,1,2}
{p4, p2, p1, p0} = ? + {0,1,3,4}
{p6, p3, p0} = ? + {0,2,3}
⟨ ⁶ᵗʰa ¹ˢᵗb ⁰ᵗʰc ⟩, (abc)₁₀ ≥ 521
⛔Avoid
2nd → 2|4|5|6
⟨⋯ 2 ⋯ ? ⋯ 4 (?+2)⟩ (?≠4,2)
#125034_v2.5
2024-05-23 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
3rd → 0
5th → a, 1st → b, a+b=1+4n
⛔Avoid
⟨ ⁴ᵗʰb ¹ˢᵗa ⟩, a > b
4th → a, 0th → b, ab=2+4n
⟨ ⁵ᵗʰa ²ⁿᵈb ¹ˢᵗc ⟩, (abc)₁₀ ≤ 410
⟦4,5⟧ ∋ 0,2,3
#125034_v2.5
2024-05-21 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
3rd → a, 0th → b, a+b=6
6th|4th|2nd|1st|0th → 4
⟨⋯ Perm(0,6) ⋯⟩
⟨⋯ a ⋯ 6 ⋯⟩, a = 0|1|2|3
3rd → a, 2nd → b, |a-b|=1
⛔Avoid
⟨⋯ ? ⋯ 6 ⋯ (?+1)⟩ (?≠5)
max ⊢3⊣ = 5
⟨⋯ Perm(1,3,4) ⋯⟩
5th|4th|3rd|0th → 1
#125034_v2.5
2024-05-21 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁰ᵗʰ↓ ⟩ after 2×⟨→⟩
5th → a, 3rd → b, ab=12
⟨⋯ ? ⋯ 0 ⋯ (?−2)⟩ (?≠2)
5th → a, 4th → b, ab=1+5n
#125034_v2.5
2024-05-19 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
3rd → a, 1st → b, |a-b|=5
⟨⋯ 2 ⋯ 3 ⋯ 0 ⋯ 6 ⋯⟩
⟨? ⋯ 6 ⋯ (?+4) ⋯⟩ (?≠2)
#125034_v2.5
2024-05-19 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
5th → a, 2nd → b, |a-b|=4
⟨⋯ 4 ⋯ 2 ⋯⟩
⛔Avoid
⟨ ⁵ᵗʰa ²ⁿᵈb ¹ˢᵗc ⟩, (abc)₁₀ ≤ 503
⟦0,2⟧ ∋ 1,3
⟨ ⁴ᵗʰa ⁰ᵗʰb ⟩, a > b
#125034_v2.5
2024-05-17 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ Perm(4,5) ⋯⟩
⟦4,6⟧ ∋ 0,1,2,5
⟨? ⋯ 5 (?−1) ⋯ 1 ⋯⟩ (?≠5,6)
⛔Avoid
Jump(1,3) ≥ 1
⟦0,4⟧ ∋ 2,3,5
#125034_v2.5
2024-05-17 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ ? ⋯ 2 ⋯ (?−4)⟩
{p5, p3, p0} = ? + {0,2,3}
⟨⋯ Perm(2,3,5) ⋯⟩
⛔Avoid
2nd → 4|5
#125034_v2.5
2024-05-16 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
Jump(3,5) = 1
Jump(0,5) = 4
⟨? ⋯ 0 ⋯ (?−1) ⋯⟩ (?≠1)
⟨ ⁶ᵗʰc ⁴ᵗʰb ³ʳᵈa ⟩, a > b > c
#125034_v2.5
2024-05-16 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
4th → a, 1st → b, a+b=3+5n
4th → a, 3rd → b, ab=1+5n
4th → a, 2nd → b, ab=0
⛔Avoid
⟨? ⋯ 2 ⋯ (?+1) ⋯⟩ (?≠2,1)
⟨ ⁵ᵗʰa ²ⁿᵈb ¹ˢᵗc ⟩, (abc)₁₀ ≤ 351
#125034_v2.5
2024-05-14 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
6th → a, 1st → b, |a-b|=3
2nd → 0|3
⟨? ⋯ 6 ⋯ (?+3) ⋯⟩ (?≠3)
max ⊢0⊣ ≤ 4
max ⊢3⊣ = 3
#125034_v2.5
2024-05-14 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
min ⊢3⊣ = 2
4th → 5
⟨? ⋯ 1 ⋯ (?+2) ⋯⟩ (?≠1)
⛔Avoid
⟨⋯ 2 ⋯ 3 ⋯⟩
#125034_v2.5
2024-05-12 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
Sim⟨ ⁶ᵗʰ4 ⁵ᵗʰ1 ⁴ᵗʰ5 ³ʳᵈ0 ²ⁿᵈ6 ¹ˢᵗ3 ⁰ᵗʰ2 ⟩ = 2
Jump(2,3) ≥ 4
⟨⋯ 6 ⋯ 4 ⋯⟩
Sim⟨ ⁶ᵗʰ6 ⁵ᵗʰ0 ⁴ᵗʰ5 ³ʳᵈ1 ²ⁿᵈ3 ¹ˢᵗ2 ⁰ᵗʰ4 ⟩ ≥ 1
⟦1,6⟧ ∋ 4
2nd → 1|2|5
⛔Avoid
⟨? ⋯ 6 (?+2) ⋯ 4 ⋯⟩ (?≠4)
5th → a, 2nd → b, |a-b|=2
#125034_v2.5
2024-05-12 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁵ᵗʰa ²ⁿᵈb ⟩, max⟦a,b⟧ = 4
5th → a, 1st → b, ab=2
⛔Avoid
Sim⟨ ⁵ᵗʰ5 ⁴ᵗʰ1 ³ʳᵈ3 ²ⁿᵈ2 ¹ˢᵗ0 ⁰ᵗʰ4 ⟩ = 1
⟨ ⁵ᵗʰa ³ʳᵈb ⟩, max⟦a,b⟧ = 4
⟨⋯ 4 ⋯ 2 ⋯⟩
#125034_v2.5
2024-05-10 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ a ⋯ 4 ⋯⟩, a = 1|2|3|5
⟨⋯ 3 ⋯ 5 ⋯ 6 ⋯⟩
⟨⋯ 4 ⋯ 3 ⋯⟩
2nd → a, 1st → b, ab=10
min ⊢2⊣ ≤ 1
#125034_v2.5
2024-05-10 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
5th → a, 1st → b, a+b=3+5n
⟦0,2⟧ ∋ 1
⟨? 4 ⋯ (?−4) ⋯ 3 ⋯⟩ (?≠4)
⛔Avoid
{p4, p1, p0} = ? + {0,1,2}
#125034_v2.5
2024-05-09 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
{p4, p3, p0} = ? + {0,2,3}
min ⊢5⊣ = 1
Jump(5,6) = 4
⛔Avoid
Jump(0,4) ≥ 1
{p6, p4, p2, p1} = ? + {0,1,2,3}
⟦4,5⟧ ∋ 2
#125034_v2.5
2024-05-09 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
5th → a, 4th → b, ab=2+5n
Jump(0,3) = 0
⛔Avoid
⟦4,5⟧ ∋ 0,2
5th|4th|2nd|0th → 2
#125034_v2.5
2024-05-07 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟦2,6⟧ ∋ 0,1,3
4th → a, 1st → b, a+b=1+6n
⟨? ⋯ 3 ⋯ (?+4) ⋯⟩
⟨ ⁴ᵗʰc ²ⁿᵈa ⁰ᵗʰb ⟩, a > b > c
3rd → 3|4|6
#125034_v2.5
2024-05-07 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
4th → a, 3rd → b, a+b=1+5n
⟨ ⁴ᵗʰc ³ʳᵈa ¹ˢᵗb ⟩, a > b > c
min ⊢4⊣ ≥ 1
⛔Avoid
min ⊢5⊣ ≥ 1
4th → a, 1st → b, a+b=4
⟨? ⋯ 5 (?−3) ⋯ 2 ⋯⟩ (?≠5)
#125034_v2.5
2024-05-05 Q1(m=6)
2024-05-05 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 3 ⋯ ? ⋯ 6 (?−3)⟩ (?≠6)
⟨⋯ 2 ⋯ 5 ⋯ 1 ⋯ 0 ⋯⟩
5th → a, 2nd → b, a+b=0+4n
⛔Avoid
⟨ ⁵ᵗʰ↑ ⟩ after ⟨→⟩
Jump(0,4) = 2
{p5, p4, p1} = ? + {0,1,2}
----- Information -----
🔲 「⟨⋯ 3 ⋯ ? ⋯ 6 (?−3)⟩ (?≠6)」
?, 6, (?−3) are three different numbers.
240 permutations match this pattern.
Examples: ⟨1340562⟩, ⟨3405261⟩, ⟨3520461⟩.
🔲 「⟨⋯ 2 ⋯ 5 ⋯ 1 ⋯ 0 ⋯⟩」
210 permutations match this pattern.
Examples: ⟨2543610⟩, ⟨2516340⟩, ⟨2356410⟩.
🔲 「5th → a, 2nd → b, a+b=0+4n」
[5th] + [2nd] = 0 | 4 | 8 | ⋯ .
960 permutations match this pattern.
Examples: ⟨2501346⟩, ⟨4120356⟩, ⟨0654213⟩.
🔳 「⟨ ⁵ᵗʰ↑ ⟩ after ⟨→⟩」
Given ⟨p6 p5 p4 p3 p2 p1 p0⟩, after “⟨→⟩” (right shift) it becomes ⟨p0 p6 p5 p4 p3 p2 p1⟩.
2520 permutations match this pattern.
Examples: ⟨1042563⟩, ⟨3241065⟩, ⟨4316025⟩.
🔳 「Jump(0,4) = 2」
There are 2 numbers between 0 and 4.
960 permutations match this pattern.
Examples: ⟨5016423⟩, ⟨0314625⟩, ⟨5214630⟩.
🔳 「{p5, p4, p1} = ? + {0,1,2}」
{ [5th], [4th], [1st] } = { ?, ?+1, ?+2 }.
720 permutations match this pattern.
Examples: ⟨0215634⟩, ⟨0641352⟩, ⟨6015423⟩.
#125034_v2.5
2024-05-05 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
4th → a, 1st → b, a+b=1+5n
⟨ ³ʳᵈc ¹ˢᵗa ⁰ᵗʰb ⟩, a > b > c
⟨? 4 ⋯ (?−2) ⋯ 3 ⋯⟩ (?≠4)
#125034_v2.5
2024-05-02 M3
P2 (老羅)
✅Match
max ⊢1⊣ ≤ 3
4th → a, 0th → b, a+b=5
⟨⋯ Perm(0,1,3) ⋯⟩
{p5, p2, p1} = ? + {0,1,2}
⛔Avoid
Sim⟨ ⁵ᵗʰ2 ⁴ᵗʰ4 ³ʳᵈ0 ²ⁿᵈ3 ¹ˢᵗ5 ⁰ᵗʰ1 ⟩ ≥ 1
Last HP: 0
Lowe the Lion defeated 老羅!
#125034_v2.5
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